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CHAPTER 3
THE PRICE OF RISK: ESTIMATING DISCOUNT RATES
To value a firm, you need to estimate its costs of equity and capital. In this
chapter, you first consider what each of these is supposed to measure, explore a simple
model for the costs and then examine the special problems associated with estimating
each for technology firms.
The cost of equity is the rate of return that investors in a firm’s equity expect to
make on their investments. Since publicly traded firms usually have thousands of
investors, the cost of equity is usually measured from the perspective of the marginal
investors in the firm – the investors most likely to be trading on the firm’s stock. The
models used to estimate the cost of equity attempt to measure the risk added by an
investment to the marginal investor’s portfolio and usually require a riskless rate and an
average market risk premium or premiums to arrive at the cost of equity.
The cost of debt is the current rate at which a firm can borrow, adjusted for any
tax benefits associated with borrowing. Firms with higher default risk should have higher
costs of debt than firms with lower default risk.
Technology firms present a particular challenge when it comes to estimating cost
of equity. Conventional approaches to estimating equity risk that are based upon stock
prices flounder given the limited and volatile price history exhibited by many of these
firms. While more mature technology firms are predominantly financed with equity, some
younger technology firms, especially start-up ventures, do carry substantial amounts of
debt. Attaching a cost of debt to the borrowings can become difficult, because these firms
are often not rated, lose money and borrow from banks.
Cost of Equity
The cost of equity is the rate of return that investors in a firm’s equity expect to
make. In this section, you see why equity risk should be measured from the perspective of
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the marginal investor in a firm’s equity, examine alternative models for measuring the
cost of equity, and then consider how best to estimate the cost of equity for technology
firms
Risk and Return Models
To estimate the cost of equity, you need to develop first a measure or measures of
risk, and then use those measures of risk to arrive at expected returns on equity
investments. You begin with a short examination of the different risk and return models
that are often used to estimate the cost of equity, and the common elements and
differences across these models. You then learn how to use these models to estimate the
cost of equity for technology firms.
Common Elements across Risk and Return Models
While there are several accepted risk and return models in finance, they all share
some common views about risk. First, they all define risk in terms of variance in actual
returns around an expected return; thus, an investment is riskless when actual returns are
always equal to the expected return.
Second, they all argue that risk has to be measured from the perspective of the
marginal investor in an asset, and that this marginal investor is well diversified.
Therefore, the argument goes, it is only the risk that an investment adds on to a
diversified portfolio that should be measured and compensated. In fact, it is this view of
risk that leads risk models to break the risk in any investment into two components. There
is a firm-specific component that measures risk that relates only to that investment or to a
few investments like it, and a market component that contains risk that affects a large
subset or all investments. It is the latter risk that is not diversifiable and should be
rewarded.
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Competing Models
While all risk and return models agree on this fairly crucial distinction, they part
ways when it comes to how measure this market risk.

The capital asset pricing model, with its assumptions that there are no transactions
cost or private information, concludes that the marginal investor hold a portfolio that
includes every traded asset in the market, and that the risk of any investment is the
risk added on to this "market portfolio." This risk is measured with a market beta,
leading to an expected return of:
Expected Return = Riskfree Rate + jM (Risk Premium on Market Portfolio)
Thus, the cost of equity in the capital asset pricing model is a function of three inputs
– the riskless rate, the risk premium on the market portfolio and the beta of the equity
investments being assessed.

The arbitrage pricing model, which is built on the assumption that assets should be
priced to prevent arbitrage, concludes that there can be multiple sources of market
risk, and that the betas relative to each of these sources measures the expected return.
Thus, the expected return is:
j= k
Expected Return = Riskfree Rate +
  (Risk Premium
j
j
)
j=1
where j = Beta of investment relative to factor j
Risk Premiumj = Risk Premium for factor j
In the arbitrage pricing model, the cost of equity is determined by the riskless rate, the
risk premiums for each of the factors in the model and the betas of an asset relative to
each factor. The factors remain unnamed and are estimated using a statistical
technique called factor analysis.

Multi-factor models, which specify macro economic variables as these factors take the
same form as the arbitrage pricing model, with multiple betas and risk premiums:
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j= k
Expected Return = Riskfree Rate +
  (Risk Premium
j
j
)
j=1
where j = Beta of investment relative to macro economic factor j
Risk Premiumj = Risk Premium for macro economic factor j
The cost of equity for a firm in a multi-factor model depends upon the riskless rate,
the risk premiums for each of the macro-economic factors and the betas for an
investment, relative to each macro-economic factor.

Regression models that relate the actual returns on stocks to observable and
measurable firm characteristics, such as market capitalization, are the final approach
to estimate the costs of equity for firms. In this approach, the regression equation is
first estimated using historical data, and then used to obtain the costs of equity for
individual firms.
Which model should you use for technology firms?
Given these choices, which, if any, of these models should you use to estimate the
cost of equity for technology firms? The first, and perhaps most significant, problem in
applying these models to valuing technology firms may lie in their perspective on risk.
The assumption that the marginal investor in a stock, i.e., the investor most likely to be
trading on the stock, is a well-diversified entity may be a difficult one to sustain for
technology firms because of the following reasons:
1. Since most technology firms are young, and the original owners continue to operate as
top managers, the proportion of stock held by the top managers at these firms is much
higher than it is in other firms. Larry Ellison at Oracle, Bill Gates at Microsoft and
Jeff Bezos at Amazon.com all continue to hold large percentages of their firms’ stock.
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2. For the smaller technology firms, there is another problem. The marginal investor
may be an individual who is not well diversified. In fact, the marginal investor may
well be a day trader whose time horizon can be measured in minutes rather than years.
How would altering the marginal investors’ characteristics change the way you measure
risk? Instead of considering only the risk that cannot be diversified away (which is what
the betas measure), you should be looking at total risk in investments if the investor is not
diversified.
Should you, therefore, abandon traditional risk and return models when looking at
technology firms? Not necessarily. Even though the largest holder of stock in many
technology firms is the owner/founder, there is little trading that occurs on this holding.
In fact, in stocks like Oracle and Microsoft, the bulk of the trading is still done by
institutional investors in the stock. This would indicate that the marginal investors,
especially in the more liquid and widely traded technology stocks, are diversified
institutional investors. When looking at less liquid technology stocks, held and traded
primarily by individuals, you should be more cautious about using the conventional
measures of risk.
If you do assume that it is, in fact, appropriate to value technology stocks using
the perspective of a well diversified investors, should you use the capital asset pricing
model, the arbitrage pricing model or the multi-factor model? The capital asset pricing
model may be the most widely used model in valuation practice, but it does contain some
significant dangers for technology stocks, especially if the market betas are estimated in
the conventional way.1 Empirical tests of the model indicate that these betas
underestimate the risk in small-capitalization stocks, relative to large capitalization
stocks. In addition, stocks with high price-earnings ratios seem to earn lower returns than
1
The conventional approach, which is described in the next section, estimates the beta for a stock by
running a regression of stock returns against a market index.
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those predicted by the capital asset pricing model over long periods. What are the
alternatives? One is to use the arbitrage pricing or multi-factor models. While these
models have the potential to better capture the risk or investing in technology firms, they
require even more historical data than the capital asset pricing model. Another is to
abandon the conventional approach to estimating market betas in the capital asset pricing
model, and consider ways of adapting the estimation process to better measure the risk of
technology stocks. The next section makes a case that the latter approach offers more
promise.
Estimation Issues
All risk and return models require three sets of inputs. The first is the riskfree rate,
the second is the appropriate risk premium or premiums for the factor or factors in the
model and the third is the beta or betas of the investment being analyzed.
I. Riskless Rate
A riskless asset is one for which the investor knows the expected returns with
certainty. Consequently, for an investment to be riskless over a specified time period
(time horizon), two conditions have to be met –

There is no default risk, which generally implies that the security has to be issued by
the government. Not all governments are viewed as default free, and this does create a
practical problem in obtaining riskless rates in some markets.

There is no uncertainty about reinvestment rates, which implies that there are no cash
flows prior to the end of your time horizon, since these cash flows have to be
reinvested at rates that are unknown today.
Short Term versus Long Term Rates
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Should you use a short-term or a long-term government bond rate as a riskless
rate? The answer depends upon when your cash flows come due. Assume, for instance,
that you are analyzing a five-year project, and you need a 5-year riskless rate. A sixmonth treasury bill is not riskless for a five-year time horizon, since there is reinvestment
risk at the end of each six-month period. In fact, neither is a five-year government bond
with coupons, since the coupons have to be reinvested, at the rates prevailing at that time,
every six months for the next 5 years. Only a 5-year zero-coupon government bond fulfils
these conditions – it has no default risk and there are no cash flows prior to the end of the
5th year.
Thus, the riskless rate is the rate on a zero coupon government bond matching the
time horizon of the cash flow being analyzed; here, since the only cash flow is the
principal on the bond coming due at maturity, there is neither default nor reinvestment
risk. In theory, this translates into using different riskless rates for each cash flow on an
investment - the 1 year zero coupon rate for the cash flow in year 1, the 2-year zero
coupon rate for the cash flow in year 2, and so on.
Matching each cash flow with a different riskless rate can be tedious, especially in
the context of a valuation, where the cash flows are often spread over ten years or more.
A simpler, though less precise, solution will suffice. You could estimate the weighted
average of when the cash flows come due by computing a duration for the cash flows in
the valuation. In fact, extending a measure of duration often used in the context of bonds,
you can estimate the duration of the cash flows in a valuation to be:
t
CF
 t * (1  r)t t
Duration of cash flows = t 1t  
CFt

t
t 1 (1  r)
Where CFt is the cash flow in year t and r is the discount rate (cost of capital, if valuing a
firm). Once the duration of the cash flows have been estimated, you can then use a
government bond with equivalent duration to derive a riskless rate. Since the cash flows
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on technology stocks tend to be weighted towards the later years (and are often negative
in the earlier years), they will have a longer duration, and this would suggest that longerterm government bond rates should be used as riskless rates when valuing these stocks.
II. Risk premium
The risk premium is clearly a significant input in all the asset pricing models. In
the following section, you begin by examining the fundamental determinants of risk
premiums, and then you look at practical approaches to estimating these premiums.
What is the risk premium supposed to measure?
The risk premium measures the “extra return” that would be demanded by
investors for shifting their money from a riskless investment to an average risk
investment. It should be a function of how risk averse investors are, and how risky they
perceive stocks (and other risky investments) to be, relative to a riskless investment.
Since each investor in a market is likely to have a different assessment of an acceptable
premium, the premium is a weighted average of these individual premiums, where the
weights are based upon the wealth the investor brings to the market. Wealthier investors
will have their risk premiums weighted more than investors with less wealth.
Estimating Risk Premiums
You look now at two ways to estimate the risk premium in the capital asset
pricing model. One is to look at the past and estimate the premium earned by risky
investments (stocks) over riskless investments (government bonds); this is called the
historical premium. The other is to use the premium extracted by looking at how
markets price risky assets today; this is called an implied premium.
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1. Historical Risk Premiums
The most common approach to estimating the risk premium is to base it on
historical data. In the arbitrage pricing model and multi- factor models, the raw data on
which the premiums are based are historical data on asset prices over very long time
periods. In the CAPM, the premium is estimated by looking at the difference between
average returns on stocks and average returns on riskless securities over an extended
period of history.
In most cases, you follow these steps to find historical risk premiums. First, you
define a time period for the estimation, which can range as far back as 1926 for U.S.
data2. Then, you calculate the average returns on stocks and average returns on a riskless
security over the period. Finally, you calculate the difference between the returns on
stocks and the riskless return and use it as a risk premium to predict future returns. When
you use historical premiums, you implicitly assume that the risk aversion of investors has
not changed across time, and that the relative riskiness of the risky portfolio (stocks) has
not changed over time, either.
In calculating the average returns over past periods, a measurement question
arises: Should you use arithmetic or geometric averages to compute the risk premium?
The arithmetic mean is the average of the annual returns for the period under
consideration, whereas the geometric mean is the compounded annual return over the
same period. The following example demonstrates the difference –
Year
0
2
Price
50
Return
The most widely used database, from Ibbotson Associates, has returns going back to 1926. Jeremy Siegel,
at Wharton, recently presented data going back to the early 1800s.
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1
100
100%
2
60
-40%
The arithmetic average return over the two years is 30%, while the geometric
average is only 9.54% (1.20.5-1=1.0954). Those who use the arithmetic average premium
argue that it is much more consistent with the framework3 of the CAPM, and a better
predictor of the risk premium in the next period. The geometric mean is justified on the
grounds that it takes into account compounding, and that it is a better predictor of the
average premium in the long term. There can be substantial differences in risk premiums
based on the choices made at this stage, as illustrated in Table 3.1. The data in the table
are based on historical data on stock, treasury bill and treasury bond returns and provide
estimates of historical risk premiums:
Table 3.1: Historical Risk Premiums for the U.S. Market
Stocks – Treasury Bills
Stocks – Treasury Bonds
Arithmetic
Geometric
Arithmetic
Geometric
1928-1999
8.73%
6.96%
7.63%
6.05%
1962-1999
6.97%
5.89%
6.06%
5.36%
1990-1999
13.29%
16.12%
10.97%
13.16%
Source: Federal Reserve
As you can see, the historical premiums can vary widely depending upon whether you go
back to 1928, 1962 or 1990, whether you use T.Bills or T.Bonds as the riskless rate, and
3
The CAPM is built on the premise of expected returns being averages, and risk being measured with
variance. Since the variance is estimated around the arithmetic average, and not the geometric average, it
may seem logical to stay with arithmetic averages to estimate risk premiums.
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whether you use arithmetic or geometric average premiums4. Although it is impossible to
prove one premium right and the others wrong, you are on safer ground assuming that::

Longer term premiums , since stock returns are volatile and shorter time periods can
provide premiums with large standard errors. For instance, the premium extracted
from 25 years of data will have a standard error5 of about 4-5%.

Long term bond rates as riskless rates, since your time horizons in corporate financial
analysis tend to be long term, and you use the treasury bond rate as your riskless rate.

Geometric average premiums, since arithmetic average premiums overstate the
expected returns over long periods6. The geometric mean yields lower premium
estimates than does the arithmetic mean, and provides a more appropriate estimate for
longer time horizons7. On this issue, however, there is significant disagreement.
Ibbotson Associates argues for the arithmetic average premium, noting that it is the
4
Booth (1999) examines both nominal and real equity risk premiums from 1871 to 1997. While the
nominal equity returns have clearly changed over time, he concludes that the real equity return has been
about 9% over than period. He suggests adding the expected inflation rate to this number to estimated the
expected return on equity.
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Assuming that returns in individual years are independent, the standard error of a 25-year estimate can be
calculated by dividing the annual standard deviation in stock prices in the US ( about 25%) by the square
root of the number of years (√25=5), yielding a standard error of 5% (25%/5) in the estimate
6
When you look at markets like the United States that have survived for 70 years without significant
breaks, you are looking at the exception. To provide a contrast, consider the other stock markets one could
have invested in 1926; many of these markets did not survive and an investor would have lost much of his
or her wealth.
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best estimate of the premium for the next period. Indro and Lee (1997) compare
arithmetic and geometric premiums, find them both wanting, and argue for a weighted
average, with the weight on the geometric premium increasing with the time horizon.
These biases would lead you closer to 6.05% which is the geometric average
premium for stocks over treasury bonds from 1928 to 1999, if you use historical
premiums. In using this premium, however, you are assuming that there are no trends in
the risk premium, and that investors today demand similar premiums to those that they
used to demand two, four or six decades ago. Given the changes that have occurred in the
markets and in the investor base over the last century, you should have serious concerns
about using this premium, especially in the context of valuation.
histret.xls: There is a dataset on the web that summarizes historical returns on
stocks, T.Bonds and T.Bills going back to 1926.
2. Implied Equity Premiums
A second approach to estimating risk premiums does not require surveys or
historical data but does assume that the overall market prices stocks correctly. Consider,
for instance, a very simple valuation model for stocks:
Value =
Expected Dividends Next Period
(Required Return on Equity - Expected Growth Rate)
This is the present value of dividends growing at a constant rate forever, developed in
chapter 5. Three of the four inputs in this model can be estimated from publicly available
7
Part of the reason for the large difference between arithmetic and geometric premium is the serial
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information - the current level of the market (value), the expected dividends next period
and the expected growth rate in earnings and dividends in the long term. The only
unknown is the required return on equity; when you solve for it, you get an implied
expected return on stocks. Subtracting out the riskless rate yields an implied equity risk
premium.
To illustrate the estimation of implied equity risk premiums, assume that the
current level of the S&P 500 Index is 900. Assume also that the expected dividends on
the index next year will be 2% of current stock prices (this is called the dividend yield),
and that the expected growth rate in earnings and dividends in the long term is 7%.
Solving for the required return on equity yields the following:
900 = (.02*900) /(r - .07)
Solving for r,
r = (18+63)/900 = 9%
If the current riskless rate is 6%, this yields a risk premium of 3%.
The advantage of this approach is that it is market-driven and current, and does
not require any historical data. It is, however, bounded by whether the valuation model
used is the right one, and by whether the inputs to that model are available and reliable.
For instance, in the above example, the use of dividends as the cash flow to equity
investors and the assumption of constant growth might lead to an implied risk premium
that is too low. Finally, the implied risk premium is based upon the assumption that the
market is correctly priced.
correlation in stock returns – good years have tended to be followed by bad years, and vice versa.
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The contrast between the implied risk premium and the historical premiums is
best illustrated by graphing out the implied premiums in the S&P 500 going back to 1960
in Figure 3.1:
Each year, you can estimate expected dividends and expected growth8, and use the level
of the index at the end of the year to estimate implied equity premiums. Note that implied
equity risk premiums are consistently lower than the historical premiums estimated in
Table 3.1. The implied premium has also decreased over time.9 At the beginning of 2000,
8
From 1980 on, analyst projections of growth as the input on growth were used. Earlier, forecast expected
growth based upon growth in the previous five years was used.
9
Pettit (1999) provides several reasons why equity risk premiums today are lower than they have been
historically and argues for a 5% risk premium.
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for instance, the implied equity risk premium was about 2%, well below the historical
premium of 6.05%.
histimpl.xls: This dataset on the web shows the inputs used to calculate the
premium in each year for the U.S. market.
implprem.xls: This spreadsheet allows you to estimate the implied equity premium in
a market.
Risk Premiums to Use in Valuing Technology Stocks
When valuing technology stocks what risk premium should you use to estimate
the cost of equity? The choice between historical and implied premiums should not be
based upon what types of stocks you are valuing but on what you believe about markets.
If you believe that markets are, on average, right, you should use implied equity risk
premiums in all your valuations. If, on the other hand, you believe that markets
collectively can become under or over valued, and that there is a tendency to revert back
to historical norms, you should use historical risk premiums. There are dangers associated
with each approach.
If you decide to use historical risk premiums in valuation, in periods such as the
current one (when implied premiums are much lower than historical premiums), you will
tend to find more stocks to be over valued than under valued. This is because large risk
premiums lead to higher discount rates (than those being assessed by the market
currently) and lower present values. This effect is exacerbated for technology stocks, in
general, and new technology stocks, in particular, because their payoffs in terms of cash
flows occur way out in the future. If, on the other hand, you decide to use the implied
equity risk premium, and the market overall is overvalued, you will tend to overvalue
stocks as well, and technology stocks more than others.
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Is there an intermediate solution? Yes. The average implied equity risk premium
between 1970 and 1999 is approximately 4%. By using this premium, you are assuming
that while markets might have been overvalued in some of these years, and undervalued
in others, it has been on average right over this period.
Finally, why don’t you use a technology stock risk premium to value technology
stocks? In the standard models of risk and return that you will be applying, the risk
premium is the premium that marginal investors demand for investing in the average risk
investment. Thus, it should remain the same for all assets. What will change across assets
is your assessment of the risk of these assets (estimated as a beta or betas).
Country Risk Premiums
Of the five companies that you will be valuing, Rediff.com poses a unique
challenge. Rediff is an internet portal directed at the Indian market. While the sheer size
of this market may be one of the more attractive parts of investing in Rediff, there is
additional exposure to risk from an emerging market in this firm that does not exist, at
least to a similar extent, when investing in Yahoo! or Amazon. Should there be an
additional risk premium added on to Rediff’s cost of equity to reflect its emerging market
status? Yes, and you should estimate it in two steps.
First, you derive a measure of India’s country risk. To arrive at this measure, you
begin with a country rating, which measures the default risk perceived in the country's
bonds. The country rating for India in June 2000 was Ba2, and the default spread for Ba2
rated bonds over the U.S. treasury bond was approximately 3%10. Second, you estimate
an additional equity risk premium for India by measuring how much more volatile the
Indian equity market is than its bond market. Using 1998-99 data, you could estimate the
annualized standard deviation in the Sensex (Indian equity index) to be 31.82% and the
10
India does not have any dollar-denominated bonds that are traded. The dollar-denominated bonds issued
by other Ba2 rated countries was used to estimate the spread over the U.S. treasury bond rate.
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annualized standard deviation in the Indian 10-year government bond to be 14.90%11.
The country risk premium for India can then be estimated as follows:
Country risk premium for India = Default spread for Country *
 Equity
 Government Bond
= 3.00% *(31.82%/14.90%) = 6.43%
This is added on to the risk premium of 4% estimated for a mature equity market,
estimated in the last part.12
How will this risk premium show up in Rediff’s cost of equity? To make this
judgment, you have to estimate Rediff’s exposure to this risk and this requires an analysis
of what it is that determines this risk and how best to measure in. In the next section, you
turn to this measurement question.
III. Betas
The beta or betas that measure risk in models of risk in finance have two basic
characteristics that you need to keep in mind during estimation. The first is that they
measure the risk added on to a diversified portfolio, rather than total risk. Thus, it is
entirely possible for an investment to be high risk, in terms of individual risk, but to be
low risk, in terms of market risk. The second characteristic that all betas share is that they
measure the relative risk of an asset, and, thus, are standardized around one. The marketcapitalization weighted average beta across all investments, in the capital asset pricing
model, should be equal to one. In any multi-factor model, each beta should have the same
property.
11
Weekly returns over 100 weeks ending July 7, 2000 were used to make both estimates.
12
For a more extensive discussion of country risk premiums, see my paper on estimating risk premiums on
my web site:
http://www.stern.nyu.edu/~adamodar/New_Home_Page/papers.html
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Keeping in mind these characteristics, you would like the beta you estimate for an
asset to measure the risk added on by that asset to a diversified portfolio. This, of course,
raises interesting follow-up questions. When you talk about diversified portfolios, are you
referring to a portfolio diversified into just equity or should you include other asset
classes? Should you look at diversifying only domestically or should you look globally?
In the CAPM, for instance, with no transactions costs, the diversified portfolio includes
all asset classes and is globally diversified. If there are transactions costs and barriers to
global investment, the market portfolio may not include all asset classes or be as globally
diversified. You can try an alternate route to answering these questions. In coming up
with a diversified portfolio, you should take the perspective of the marginal investor in
the market. The extent to which that marginal investor is diversified should determine the
composition of the index to use in estimating betas.
In the section that follows, you consider two approaches to estimating betas. The
first is the regression approach, where historical stock returns are used to compute the
beta of a stock. The other is the bottom-up approach, where you estimate the beta by
breaking a firm down into individual businesses, and estimating the betas of these
businesses.
I. The Regression (or Top-down) Approach
The textbook description of beta estimation is simple. The beta for an asset can be
estimated by regressing the returns on any asset against returns on an index representing
the market portfolio, over a reasonable time period, as shown in Figure 3.2.
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Figure 3.2: Regression of Returns on Stock against Returns on Market Index
In this figure, the returns on the asset represent the Y variable, and the returns on the
market index represent the X variable. Note that the regression equation that you obtain is
as follows:
Rj = a + b R M
Where Rj is the return on investment j, and RM is the return on the market index. The
slope of the regression 'b" is the beta, because it measures the risk added on by that
investment to the index used to capture the market portfolio. In addition, it also fulfils the
requirement that it be standardized, since the weighted average of the slope coefficients
estimated for all of the securities in the index will be one.
The Limitations of Regression Betas for Technology Firms
While you can use the regression approach to estimate betas for technology firms,
these betas are likely to be affected by three problems that while not unique to these firms
are exaggerated in their case.
1. Estimation Choices and Betas
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The regression betas will vary widely depending upon how the regression is set up
and run. Consider the case of Cisco. You could estimate Cisco’s beta relative to the S& P
500, the index most widely by beta estimation services in the United States, and get the
regression shown in Figure 3.3
Figure 3.3: Beta Estimate for Cisco: S&P 500
This regression uses monthly returns over 76 months to arrive at this estimate.
Alternatively, you could have estimated Cisco’s beta relative to the index of the exchange
on which it is traded – the NASDAQ. The regression output is shown in Figure 3.4.
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Figure 3.4: Beta Estimate for Cisco: NASDAQ
Note how different the betas are with the two indices - 1.09 with the NASDAQ versus
1.39 with the S&P 500. Which one is the right index? In the capital asset pricing model,
the index that comes closer to the “market portfolio,” which contains all traded assets in
proportion to their market value would be the better index. From that perspective, the
S&P 500 would be the better choice, since it includes the 500 largest market
capitalization firms in the United States. But, you could legitimately have estimated
Cisco’s beta against other indices such as the Wilshire 5000 (which includes far more
U.S, stocks) or the Morgan Stanley Capital Index (which has a better claim as an index
that represents a global market portfolio). The betas would have been very different from
the betas estimated above.
The choice of index is but one of the many choices that can affect the beta
estimate. There are at least two others. One is the period over which you estimate the
beta. Approximately six years of history were used in the two beta estimates above, but
there is no consensus on this, with some services using only 2 years of history. The other
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is the return interval used to estimate returns. Monthly returns were used in the two
estimates above, but daily, weekly, quarterly or annual returns could also have been used.
Table 3.2 reports the beta estimate for Cisco, relative to the S&P 500, as a function of
these choices.
Table 3.2: Beta Estimates for Cisco
Daily
Weekly
Monthly
Quarterly
2 years
1.72
1.74
1.82
2.70
5 years
1.63
1.70
1.45
1.78
Source: Bloomberg
It should be troubling, from the perspective of valuation, that the regression technique can
yield beta estimates ranging from 1.45 to 2.70.
2. The Noise Problem
The beta estimate from the regression is noisy, and the range that emerges for the
beta is large. Figure 3.5 reports the beta estimate for Amazon.com. Since it has been
traded only since 1997, three years of monthly returns were used to make this estimate:
Figure 3.5: Beta Estimate for Amazon.com
23
Source: Bloomberg
The beta estimate for Amazon of 2.67 comes with a standard error of
1.00. If you assume that the beta estimate is normally distributed, this would imply that
the true beta for Amazon would lie between 1.67 (2.67- one standard error) and 3.67
(2.67 + one standard error) with 67% confidence. While beta estimates for all firms come
with standard errors, they tend to be much larger for technology firms, partly because of
their limited histories and partly because of the volatility of their stock prices.
In fact, the beta estimate for Ariba has to be based upon less than one year of data.
Rediff.com, as an initial public offering, represents the limiting case for this problem,
since it has no public history. Its beta cannot be estimated using the regression approach.
3. The Problem of Firms Changing over Time
Even if a stock does not dominate the index, and the regression beta has a low
standard error, there is a final problem with regression beta estimates. They are based
upon historical data, and firms change over time. Technology firms change more than
most since the technology evolves, revenues grow exponentially and the firm’s basis
product mix often changes. In addition, these firms often acquire other firms to grow.
Thus, the regression reflects the firm's characteristics, on average, over the period of the
estimation rather than the firm as it exists today. Again, this problem is obvious with both
Amazon and Cisco. Amazon, over the four years of its history, has seen its revenues
change dramatically from $16 million in 1996 to $1.6 billion in 1999. Clearly, it was a
very different firm in 1999 than it was in 1996.
II. Bottom-up Betas
The beta of a firm might be estimated from a regression, but it is determined by
fundamental decisions that a firm takes on where to invest, what type of cost structure it
plans to maintain and how much debt it takes on. The alternative approach to beta
24
estimation considers these fundamentals and is the bottom-up approach to beta
estimation. To understand this approach, you can begin be considering the fundamentals
that determine betas and then provide a framework for estimating bottom-up betas.
Determinants of Betas
The beta of a firm is determined by three variables -(1) the type of business(es) the
firm is in, (2) the degree of operating leverage in the firm and (3) the firm's financial
leverage. While much of the discussion in this section is couched in terms of CAPM
betas, the same analysis can be applied to the betas estimated in the APM and the multifactor model as well.
1. Type of Business
Since betas measure the risk of a firm relative to a market index, the more
sensitive a business is to market conditions, the higher is its beta. Thus, other things
remaining equal, cyclical firms can be expected to have higher betas than non-cyclical
firms. Other things remaining equal, then, companies involved in housing and
automobiles, two sectors of the economy which are very sensitive to economic
conditions, will have higher betas than companies which are in food processing and
tobacco, which are relatively insensitive to business cycles.
Building on this point, you can see that the degree to which a product’s purchase
is discretionary affects the beta of the firm manufacturing the product. “Discretionary”
refers to the capacity of customers of the firm to delay, defer or not buy the product or
service, if their income drops. Technology firms that produce products that are nondiscretionary to their customers should have lower betas than technology firms that
produce discretionary products. For instance, you would expect a firm that manufactures
expensive add-ons for computers to have a higher beta than a firm that manufactures
25
computers, and a firm that produces computer games to have a higher beta than a firm
that produces virus protection programs.
There is also a link between a firm’s growth potential and the discretionary nature
of its products. If a significant portion of a firm’s value comes from expected future
growth, you would expect it to have a higher beta than a firm that gets most of its value
from existing assets. This is because a high-growth firm has to attract new customers to
its products or get existing customers to use more of its products, and the extent to either
occurs may depend upon how well customers are doing.
b. Degree of Operating Leverage
The degree of operating leverage is a function of the cost structure of a firm, and is
usually defined in terms of the relationship between fixed costs and total costs. A firm
that has high operating leverage (i.e., high fixed costs relative to total costs), will also
have higher variability in earnings before interest and taxes (EBIT) than would a firm
producing a similar product with low operating leverage. Other things remaining equal,
the higher variance in operating income will lead to a higher beta for the firm with high
operating leverage.
While operating leverage affects betas, it is difficult to measure the operating
leverage of a firm, at least from the outside, since fixed and variable costs are often
aggregated in income statements. It is possible to get an approximate measure of the
operating leverage of a firm by looking at changes in operating income as a function of
changes in sales.
Degree of Operating leverage = % Change in Operating Profit / % Change in Sales
26
For firms with high operating leverage, operating income should change more than
proportionately, when sales change.
What is the relevance for technology firms? Many new technology firms have
significant fixed costs associated with setting up infrastructure and developing new
products. Once these costs have been incurred, however, the variable costs are often low.
America Online, for instance, faces very little additional costs when it adds a new
subscriber, having used its resources to develop a communication network in prior years.
For firms like Cisco and Microsoft, research and development expenses can be viewed as
a fixed costs, since the failure to do research can be disastrous for future growth. These
high fixed costs should lead to higher betas for technology firms. Furthermore, since there
are economies of scale associated with size, you would expect smaller technology firms
to have much higher betas than larger technology firms.
c. Degree of Financial Leverage
Other things remaining equal, an increase in financial leverage will increase the
equity beta of a firm. Intuitively, the obligated payments on debt increase the variance in
net income, with higher leverage increasing income during good times and decreasing
income during economic downturns. If all of the firm's risk are borne by the stockholders
(i.e., the beta of debt is zero)13, and debt has a tax benefit to the firm, then,
L = u (1 + (1-t) (D/E))
where
13
If debt has market risk (i.e., its beta is greater than zero), this formula can be modified to take it into
account. If the beta of debt is D , the beta of equity can be written as:
27
L = Levered Beta for equity in the firm
u = Unlevered beta of the firm ( i.e., the beta of the firm without any debt)
t = Corporate tax rate
D/E = Debt/Equity Ratio
The unlevered beta of a firm is determined by the types of the businesses in which it
operates and its operating leverage. Thus, the equity beta of a company is determined
both by the riskiness of the business it operates in, as well as the amount of financial
leverage risk it has taken on.
Technology firms tend to be lightly levered. Thus, very seldom can debt be
fingered as the culprit when a firm has a high beta. Given the high risk inherent in their
underlying businesses, technology firms tend to have high unlevered betas. Borrowing
money will only exaggerate the impact of leverage and push the betas of these firms to
even higher levels.
This spreadsheet allows you to estimate the unlevered beta for a firm and compute
the betas as a function of the leverage of the firm.
Estimating Bottom-up Betas
Breaking down betas into their business, operating leverage, and financial
leverage components provides you with an alternative way of estimating betas, where you
do not need past prices on an individual firm or asset to estimate its beta.
To develop this alternative approach, you need to introduce an additional feature
that betas possess that proves invaluable. The beta of two assets put together is a
L = u (1+(1-t)(D/E)) - D (D/E)
28
weighted average of the individual asset betas, with the weights based upon market value.
Consequently, the beta for a firm is a weighted average of the betas of all of different
businesses it is in. Thus, the bottom-up beta for a firm, asset or project can be estimated
as follows.
(1) Identify the business or businesses that make up the firm, asset or project.
(2) Estimate the unlevered beta(s) for the business or businesses that the firm is involved
in. The simplest approach uses these unlevered betas directly, without adjusting for
any differences between the firm being analyzed and the average firm in the sector.
When you do this you implicitly assume that all firms in a sector have the same
operating leverage. Given that smaller firms tend to have a greater proportion of fixed
costs than larger firm, a more discriminating approach requires that you do one of the
following:

Assume that market capitalization and operating leverage are correlated, and use
the unlevered beta of firms with similar market capitalization in estimating the
unlevered beta.

Calculate the operating leverage of the division or firm being analyzed and
compare it to the operating leverage of comparable firms. If the firm being
analyzed has a higher proportion of fixed costs than the comparable firms, the
unlevered beta should be adjusted upwards (downwards).
(3) To calculate the unlevered beta for the firm, take a weighted average of the unlevered
betas, using the estimated values of the different businesses that the firm is involved
in. If the values are not available, use a reasonable proxy such as operating income or
revenues.
29
(4) Calculate the leverage for the firm, using market values if available. If not, use the
target leverage specified by the management of the firm or industry-typical debt
ratios.
(5) Estimate the levered beta for the firm (and each of its businesses) using the unlevered
beta from step 3 and the leverage from step 4.
Advantages of Bottom-up Betas
This approach provides much better beta estimate for firms for three reasons. The
first is that you estimate the unlevered betas, by sector, by averaging across regression
betas. While regression betas are noisy and have large standard errors, averaging across
regression betas reduces the noise in the estimate. In fact, the standard error of the
average beta can be approximated as follows:
Standard Error Average Beta =
Average Standard ErrorBeta Estimate
n
where n is the number of firms in the sector. To illustrate, consider the software sector.
The average standard error for betas estimates in this sector is 0.50, and that there are 225
firms in the sector. The standard error of the average beta estimate can then be estimated
as follows:
Standard Error Average Software Bet a =
Average Standard ErrorBeta Estimate
0.50

 0.03
n
225
The second advantage is that the beta estimates reflect the firm as it exists today, since it
is computed based upon current weightings for different businesses. In fact, expected
changes in business mix can be reflected in beta estimates quite easily with bottom-up
betas. The final advantage is that the levered beta is computed using the current financial
leverage of the firm, rather than the average leverage over the period of the regression.
Thus, the beta can be estimated more accurately for firms that have changed their
debt/equity ratio in recent periods.
30
This data set on the web has updated betas and unlevered betas by business
sector in the United States.
Illustration 3.1: Estimating Bottom-up Betas
The betas for the firms in the analysis can be estimated using the bottom up
approach and the average betas for the sectors in which each of the firms operate.
1. Bottom Up Beta for Cisco
To estimate Cisco’s bottom-up beta, it is assumed that Cisco is in a single
business (telecomm services) and the following firms could be viewed as comparable
firms.14
Company Name
Beta Market Cap $ (Mil) Total Debt $ (Mil)
3Com Corp.
1.35
$
16,620.70
$
45.00
ADC Telecom.
1.40
$
21,498.00
$
46.20
Alcatel ADR
0.90
$
336,934.70
$
4,793.90
Ciena Corp.
1.70
$
18,395.90
$
Comverse Technology
1.45
$
13,499.20
$
301.10
E-TEK Dynamics
$
15,517.00
$
28.90
JDS Uniphase
1.60
$
65,566.00
$
Lucent Technologies
1.30
$
201,173.20
$
7,026.00
Nortel Networks
1.40
$
164,284.30
$
1,665.00
Tellabs, Inc.
1.75
$
28,664.50
$
2.80
Average
1.43
Source: Value Line
The average levered beta for the comparable firms is 1.43. The debt to equity ratio is
computed for the comparable firms, using the cumulated market value of equity
14
Morningstar.com’s categorization of comparable firms is used to develop this list.
31
($8821,54) and the cumulated market value of debt ($13,909) of the firms.15 This average
value is less affected by extreme values for the debt to equity ratio that individual firms
may possess. The unlevered beta can then be estimated as follows:16
Unlevered Beta = 1.43/ (1+(1-0.3056)*(13909/882154)) = 1.412
This beta is affected by the fact that these firms have cash on their balance sheets, since
cash has a beta of zero. The proportion of firm value (market value of equity plus debt)
that was cash is computed to be 1.41%, and an unlevered beta for the business is
estimated as follows:17
Unlevered beta (cleansed of cash)
= Unlevered Beta / (1 – Cash/ Firm Value)
= 1.412/(1-.0141) = 1.43
To estimate Cisco’s bottom-up beta, Cisco’ market values of equity and debt are used:
Market Value of Equity = $ 64.88/share * 6890 million = $ 446,989 million
Estimated Market Value of Debt = $ 0
Bottom-up Beta for Cisco = 1.43
Note that this will be the beta that you use to value Cisco’s operating assets. The cash is
viewed as a separate asset that is added on to the value of the operating assets.
15
There are two measurement alternatives. One is to compute the unlevered beta for each firm and to
average the unlevered betas. The other is to compute the debt to equity ratio for each firm and take the
average debt to equity ratio.
16
The average effective tax rate for the comparable firms of 30.56% is used to estimate the unlevered beta
17
I do this because cash balances can be different for different firms in the same business.
32
2. Bottom Up Betas for Ariba , Amazon.com and Rediff.com
Ariba and Amazon.com are considered internet firms but they operate in
businesses where they compete with more conventional firms (brick and mortar, so to
speak). For instance, Amazon.com can be considered a specialty retailer that delivers its
products online, just as Ariba can be considered a firm that provides business services
that operates on the internet. To estimate Ariba and Amazon.com’s betas, therefore, you
can look at two groups of comparable firms. First, you can look at internet firms as a
group, and estimate the betas for firms that offer business services online (for Ariba) and
for internet retailers (for Amazon). Second, you can estimate the betas of firms in the
businesses that Ariba and Amazon.com operate in – business services and specialty
retailing. Table 3.3 summarizes the estimates of the unlevered betas for each group:
Table 3.3:Unlevered Beta Estimates for Sectors
In business
Ariba
Amazon.com
Internet firms
1.78
1.61
Conventional firms
1.18
1.01
Source: Value Line
To value these firms, it is assumed that Ariba and Amazon are currently viewed by
investors as internet firms first and business service or retail firms second, and the betas
for internet firms are used as their betas for the next 5 years. As both firms become larger,
the fact they deliver their products and services online will become secondary and their
primary businesses will come to the fore. Consequently, the betas will be moved towards
those of conventional firms after year 5.18 Since Amazon does have debt outstanding, the
18
You adjust betas from year 6 through 10 to move them from internet levels to conventional levels.
33
levered beta for the next 5 years to is estimated to be 1.74, based upon its market value of
equity (at the time of the analysis) of $17.26 billion and the market value of debt of
$1.345 billion.
Amazon’s levered beta = 1.61 ( 1 + (1-.00) (1.345/17.26)) = 1.74
Azero percent tax rate is used, since Amazon is losing money and has considerable
net operating losses to carry forward.
For Rediff.com, you face a tougher decision. The firm operates an internet portal and,
thus, would not have existed prior to the online boom, but it does make its money in
conventional ways – from other firms advertising on its site. Portals try to attract
customers by providing content or services (such as search engines) for free, and charge
for advertising based upon the number visitors they attract. Fundamentally, therefore, they
do not differ from newspapers and magazines, which base their advertising rates on
circulation and readership. As with Ariba and Amazon, you begin by using the average
beta for internet portals that are publicly traded as the beta for Rediff,com; the average
beta of these firms in 2000 was 1.90. You then move the beta of Rediff.com towards the
average for publishing and newspaper firms as the firm matures; the average beta for
these firms in 2000 was 1.07. There is the real possibility that Rediff could evolve into a
different kind of online business, becoming an online exchange or expanding into online
retailing. Since all of these businesses currently have high betas (1.7-1.9), it should not
make a significant difference in the near-term cost of equity.
3. Bottom-up Beta for Motorola
Unlike Cisco, Ariba and Amazon.com, Motorola operates in two different businesses
– telecomm equipment and semiconductors. Since the beta for Motorola is a weighted
34
average of the betas of these two businesses, you first have to compute the weights to
attach to each business. In theory, the weights should be market value weights, but the
divisions are not traded. You have three choices. You could use the operating income that
Motorola reports for each business to weight them. While this approach has intuitive
appeal, it can lead to negative weights for any business that is currently generating
negative operation income. Alternatively, you could use the revenues generated by each
business to weight them. While this approach is simple and the weights are always
positive, you are implicitly assuming that the margins are equal across businesses. In the
third approach, you estimate the revenues in each business first, and then multiply them
by the average Value/Sales ratio prevalent in publicly traded firms in that business to
estimate an approximate value for each business. You then use these values to weight the
businesses:
Table 3.4: Motorola : Bottom-up Beta
Segment
Revenues
Value/Sales
Estimated Value Proportion
Unlevered Beta
Telecom Equipment
$ 28,472.00
6.69
$
190,478
71.76%
1.09
Semiconductors
$ 7,370.00
10.17
$
74,953
28.24%
1.32
Motorola
$ 35,842.00
Bottom-up Unlevered beta =
1.1563
Source: Motorola 10-K
The equity beta can then be estimated using the current financial leverage for
Motorola as a firm. Combining the market value of equity of $ 73.306 billion and the
value of debt of $ 4.583 billion, and using a 35% tax rate for the firm, you arrive at the
current beta for Motorola.
Equity Beta for Motorola = 1.1563(1+(1-.35)(4.583/73.306)) = 1.203
IV. Estimating the Cost of Equity
35
Having estimated the riskless rate, the risk premium(s) and the beta(s), you can
now estimate the expected return from investing in equity at any firm. In the CAPM, this
expected return can be written as:
Expected Return = Riskless Rate + Beta * Expected Risk Premium
where the riskless rate would be the rate on a long-term government bond, the beta would
be either the historical, fundamental or accounting betas described above, and the risk
premium would be either the historical premium or an implied premium.
In the arbitrage pricing and multi-factor model, the expected return would be
written as follows:
j n
Expected Return = Riskless Rate +
  * Risk Premium
j 1
j
j
where the riskless rate is the long term government bond rate, j is the beta relative to
factor j, estimated using historical data or fundamentals, and Risk Premiumj is the risk
premium relative to factor j, estimated using historical data.
The expected return on an equity investment in a firm, given its risk, has
implications for both equity investors in the firm and the managers of the firm. For equity
investors, it is the rate they need to earn to be compensated for the risk they have taken in
investing in the equity of the firm. If, after analyzing an investment, they conclude they
cannot make this return, they would not buy this investment; alternatively, if they decide
they can make a higher return, they would make the investment. For managers in the firm,
the return investors need to make to break even on their equity investments becomes the
return they have to try to deliver to these investors. In other words, this is the cost of
equity to the firm.
36
Illustration 3.2: Estimating the Cost of Equity
In the following analysis, you estimate the cost of equity for the firms you are
valuing, using the CAPM. In doing so, you use the bottom-up betas since they reflect best
the true riskiness of these firms. Table 3.5 summarizes these estimates:
Table 3.5: Cost of Equity Calculations(for next 5 years)
Motorola
Cisco
Amazon
Ariba
Rediff
Bottom-up Unlevered Beta
1.1563
1.43
1.61
1.78
1.90
Bottom-up Beta
1.203
1.43
1.74
1.78
1.90
Riskless Rate
6.00%
6.00%
6.00%
6.00%
6.00%
Risk Premium
4.00%
4.00%
4.00%
4.00%
10.43%
Cost of Equity
10.81%
11.72%
12.77%
13.12%
25.82%
Note that the riskless rate and risk premium are the same for each of the first four firms.
The only input that varies across these firms is the beta, with the higher beta stocks
having higher costs of equity than the lower beta firms. The risk premium for Rediff.com
is higher because it includes the country risk premium of 6.43% for India, leading to a
much higher cost of equity for the firm. The cost of equity is estimated in U.S. dollar
terms to reflect the fact that the initial public offering was in the United States.19
19
The dollar cost of equity can be converted into an Indian rupee cost of equity fairly easily by taking into
account the difference in inflation rates in the two countries. For instance, using expected inflation rates of
6% for India and 3% in the United States, you can estimate the rupee cost of equity for Rediff.com as
follows:
Cost of equity (in Rs) = (1 + $ Cost of equity4) (1+Inflation rateIndia)/(1+ Inflation rateUS) -1
= 1.2582 (1.06/1.03) -1= 29.49%
37
V. Risk, Cost of Equity and Private Firms
Implicit in the use of beta as a measure of risk is the assumption that the marginal
investor in equity is a well diversified investor. While this is a defensible assumption
when analyzing publicly traded firms, it becomes much more difficult to sustain for
private firms. The owner of a private firm generally has the bulk of his or her wealth
invested in the business. Consequently, he or she cares about the total risk in the business,
rather than just the market risk.
There are three ways of estimating the cost of equity for a private firm, with
undiversified owners:
1. Assume that the business is run with the near-term objective of selling to a large
publicly traded firm, or making an initial public offering; this is often the case with
young technology firms. In such a case, it is reasonable to use the market beta and
cost of equity that comes from it.
2. Add a premium to the cost of equity to reflect the higher risk created by the owner’s
inability to diversify. (This may help explain the high returns some venture capitalists
demand on their equity investments in fledgling businesses)
3. Adjust the beta to reflect total risk rather than market risk. This adjustment is a
relatively simple one, since the R squared of the regression measures the proportion
of the risk that is market risk.
Total Beta = Market Beta / √R squared
In the case of Rediff.com, where the market beta is 1.90 and the average R-squared of the
comparable publicly traded firms is 16%, this would lead to a total beta estimate of 4.75,
resulting in a cost of equity of 55.54% for Rediff.com as a private firm. However, the cost
38
of equity you use to value the initial public offering is based upon the market beta, since
the potential investors in the initial public offering are likely to be well diversified.
What if you were a venture capitalist analyzing an equity investment in a private
firm? The cost of equity you would use will fall somewhere between the cost of equity
that you estimate based upon the market beta and the cost of equity you obtain from a
total beta, depending upon how diversified the venture capitalist is. Most venture
capitalists are diversified across firms in a sector – i.e., they are sector focused – but not
diversified across sectors. Consequently, their costs of equity will be higher than those
estimated using a market beta.
From Cost of Equity to Cost of Capital
While equity is undoubtedly an important and indispensable ingredient of the
financing mix for every business, it is but one ingredient. Many businesses finance some
or much of their operations using debt or some security that is a combination of equity
and debt. The costs of these sources of financing are generally different from the cost of
equity, and the cost of financing for a firm should reflect their costs as well, in proportion
to their use in the financing mix. Intuitively, the cost of capital is the weighted average of
the costs of the different components of capital used by a firm to fund its operations.
Estimating the cost of capital for a technology firm is complicated by three factors:

These firms are disproportionately dependent on equity for capital. In fact, some of
these firms are entirely financed with equity.

The firms that use public debt tend to use hybrid securities, such as convertible bonds,
to raise funds.
39

Smaller technology firms have bank borrowings, and are often not rated by the ratings
agencies.
In this section, you consider first how best to estimate the cost of debt for technology
firms and how to deal with hybrid securities in cost of capital calculations.
Calculating the Cost of Debt
The cost of debt measures the current cost to the firm of borrowing funds to
finance projects. In general terms, it is determined by the following variables:
(1) The current level of interest rates: As the level of interest rates increases, the cost of
debt for firms will also increase.
(2) The default risk of the company: As the default risk of a firm increases, the cost of
borrowing money will also increase.
(3) The tax advantage associated with debt: Since interest is tax deductible, the after-tax
cost of debt is a function of the tax rate. The tax benefit that accrues from paying interest
makes the after-tax cost of debt lower than the pre-tax cost. Furthermore, this benefit
increases as the tax rate increases.
After-tax cost of debt = Pre-tax cost of debt (1 - tax rate)
Estimating the Default Risk and Default Spread of a firm
The simplest scenario for estimating the cost of debt occurs when a firm has long
term bonds outstanding that are widely traded. The market price of the bond, in
conjunction with its coupon and maturity can serve to compute a yield you use as the cost
of debt. For instance, this approach works for a firm like AT&T that has dozens of
outstanding bonds that are liquid and trade frequently.
40
Many firms have bonds outstanding that do not trade on a regular basis. Since these
firms are usually rated, you can estimate their costs of debt by using their ratings and
associated default spreads.
Some companies choose not to get rated. Many smaller firms and most private
businesses fall into this category. While ratings agencies have sprung up in many
emerging markets, there are still a number of markets where companies are not rated on
the basis of default risk. When there is no rating available to estimate the cost of debt,
there are two alternatives:

Recent Borrowing History: Many firms that are not rated still borrow money from
banks and other financial institutions. By looking at the most recent borrowings made
by a firm, you can get a sense of the types of default spreads being charged the firm
and use these spreads to come up with a cost of debt.

Estimate a synthetic rating: An alternative is to play the role of a ratings agency and
assign a rating to a firm based upon its financial ratios; this rating is called a synthetic
rating. To make this assessment, you begin with rated firms and examine the financial
characteristics shared by firms within each ratings class. To illustrate, table 3.6 lists
the range of interest coverage ratios for riskier non-financial service firms in each
S&P ratings class20.
Table 3.6: Interest Coverage Ratios and Ratings
Interest Coverage Ratio Rating
> 12.5
AAA
20
This table was developed in early 1999, by listing out all rated firms, with market capitalization lower
than $ 2 billion, and their interest coverage ratios, and then sorting firms based upon their bond ratings. The
ranges were adjusted to eliminate outliers and to prevent overlapping ranges.
41
9.50 - 12.50
7.50 – 9.50
6.00 – 7.50
4.50 – 6.00
3.50 – 4.50
3.00 – 3.50
2.50 – 3.00
2.00 - 2.50
1.50 – 2.00
1.25 – 1.50
0.80 – 1.25
0.50 – 0.80
< 0.65
AA
A+
A
ABBB
BB
B+
B
BCCC
CC
C
D
Source: Compustat
Now consider Motorola. It has an interest coverage ratio of 10.54. Based on this ratio,
you would assess a “synthetic rating” of AA for the firm. This approach can be expanded
to allow for multiple ratios and qualitative variables, as well.
Once you have a bond rating for a firm, the cost of borrowing can be estimated by
adding a default spread, based upon the rating, to the riskless rate. Allowing for a default
spread of 0.50% for AA rated firms and a riskless rate of 6%, you estimate a pre-tax cost
of debt of 6.50% for Motorola.
While this approach works reasonably well for firms that have established income
streams, it can be difficult to get a good synthetic rating for young firms based upon
current operating income. The ratings of these firms reflect expecations about the future,
and the operating income can usually be expected to change dramatically over the next
few years. In these cases, a synthetic rating can be estimated based upon the expected
interest coverage ratio over the next few years, rather than the current interest coverage
ratio.
Illustration 3.3: Estimating the Cost of Debt for Amazon
42
Amazon.com has $1,480.66 billion in debt outstanding. While this is a relatively
small amount of debt, given its market value of equity is $17.236 billion, it is still
surprising since Amazon reported an operating loss of $276 million in 1999. To estimate
the cost of debt for Amazon, you could use its current bond rating of B, assigned to it by
Standard and Poor. Alternatively, you could estimate the interest coverage ratio for the
firm and compute a synthetic rating. With a negative operating income, the interest
coverage ratio will be negative, yielding a synthetic rating of D.
How do you reconcile the two ratings (B from the ratings agency and D from the
synthetic rating) and which one should you use in your analysis? The ratings agencies are
clearly assuming that Amazon’s operating income in future years will be higher and, thus,
would justify their higher rating. To estimate an equivalent synthetic rating, you used the
projections of operating income that you have for Amazon for the next 3 years, and
compute an average interest coverage ratio based upon the average operating income over
the next 5 years:
Average operating income (next 3 years) = $ 270 million
Interest Expenses (current) = $ 84.57 million
Interest coverage ratio = 270/84.57 = 3.19
Synthetic rating = BB
Default spread for BB rated bonds = 2.00%
Pre-tax cost of debt for Amazon.com = Riskless Rate + Default spread = 6%+2% = 8%
After-tax cost of debt for Amazon.com = 8% (since firm does not pay taxes currently)
The cost of debt for Amazon will change over time for two reasons. One aspect is that
Amazon will start paying taxes in two years, and the interest expense will yield a tax
savings. The other issue is that Amazon will become a larger, more stable firm over the
43
next few years, leading to better ratings and lower default spreads. The following table
summarizes the cost of debt estimates for Amazon over the next 10 years:
Table 3.7: Pre-tax and After-tax Cost of Debt - Amazon
Year
1
2
3
4
5
6
7
8
9
10
Cost of Debt Tax Rate After-tax Cost of debt
8.00%
0.00%
8.00%
8.00%
0.00%
8.00%
8.00% 18.40%
6.53%
8.00% 35.00%
5.20%
8.00% 35.00%
5.20%
7.80% 35.00%
5.07%
7.75% 35.00%
5.04%
7.67% 35.00%
4.98%
7.50% 35.00%
4.88%
7.00% 35.00%
4.55%
Note that the after-tax cost of debt declines from 8% in year 1 of the analysis to 4.55% in
year 10.21
ratings.xls: This spreadsheet allows you to estimate the synthetic rating and cost of
debt for any firm.
Calculating the Cost of Hybrid Securities
While debt and equity represent the fundamental financing choices available for
firms, there are some types of financing that share characteristics with both debt and
equity. These are called hybrid securities. In this section, you consider how best to
estimate the costs of two such securities – preferred stock and convertible stock.
Preferred Stock
Preferred stock shares some of the characteristics of debt - the preferred dividend
is pre-specified at the time of the issue and is paid out before common dividend -- and
44
some of the characteristics of equity - the payments of preferred dividend are not tax
deductible. Preferred stock is generally issued in perpetuity and the cost of preferred
stock can be written as follows:
kps = Preferred Dividend per share/ Market Price per preferred share
This approach assumes the dividend is constant in dollar terms forever and that the
preferred stock has no special features (convertibility, callability etc.). If such special
features exist, they will have to be valued separately to estimate the cost of preferred
stock. In terms of risk, preferred stock is safer than common equity, because preferred
dividends are paid before dividends on common equity. It is however, riskier than debt
since interest payments are made prior to preferred dividend payments. Consequently, on
a pre-tax basis, it should command a higher cost than debt and a lower cost than equity.
Convertible Bonds
A convertible bond is a bond that can be converted into equity, at the option of
the bondholder. A convertible bond can be viewed as a combination of a straight bond
(debt) and a conversion option (equity). Technology firms are heavy users of convertible
debt, for two reasons:
1. The conversion option on the bond increases its price and reduces the coupon rate on
the bond. This allows firms with low operating cash flows to service debt payments.
2. The high volatility in stock prices that characterizes many technology firms works in
their favor by increasing the value of conversion options on convertible bonds.
What is the cost of a convertible bond? The simplest approach to analyzing a
convertible bond is to break it down into debt and equity components and treat the
21
The tax rate is explained in fuller detail in the chapter 5.
45
components separately.
There are two ways in which this break down can be
accomplished:

An option pricing model can be used to value the conversion option, which is treated
as equity. The difference between the price of the convertible bond and the conversion
option value is then treated as debt.

The convertible bond can be valued as if it were a straight bond, using the stated
coupon rate and maturity for the valuation, and this value is treated as debt. The
difference between the convertible bond price and this value is the value of the
conversion option and treated as equity.
Illustration 3.5: Breaking down a convertible bond into debt and equity components:
Amazon Inc
In 1999, Amazon Inc issued convertible bonds with a coupon rate of 4.75% and a
ten-year maturity. Since the firm was losing money, it was rated CCC+ by S&P and
would have had to pay 11% if it had issued straight bonds at the same time. The bond
were issued at a price that was 98% of par, and the total par value of the convertible bond
issue was $ 1.25 billion. Each convertible bond (with a face value of $1,000) can be
broken down into straight bond and conversion option components.
Straight Bond component = Value of a straight 4.75% coupon bond due in 10 years with a
11% interest rate = $ 636 (assuming semi-annual coupons)
Conversion Option
= $ 980 - $ 636 = $ 344
The straight bond component of $636 is treated as debt, and has the same cost as the rest
of debt. The conversion option of $ 344 is treated as equity, with the same cost of equity
as other equity issued by the firm. For the entire bond issue of $ 1.25 billion, the value of
debt is $ 795 million, and the value of equity is $ 430 million.
46
Calculating the Weights of Debt and Equity Components
The weights assigned to equity and debt in calculating the weighted average cost
of capital have to be based on market value, not book value. This is so because the cost of
capital measures the cost of issuing securities – stocks as well as bonds -- to finance
projects, and these securities are issued at market value, not at book value.
There are three standard arguments against using market value, and none of them
are convincing. First, there are some financial managers who argue that book value is
more reliable than market value because it is not as volatile. While it is true that book
value does not change as much as market value, this is more a reflection of book value’s
weakness rather than its strength, since the true value of the firm changes over time as
both firm-specific and market information is revealed. Market value, with its volatility, is
still a much better reflection of true value than is book value.22
Second, the defenders of book value also suggest that using book value rather than
market value is a more conservative approach to estimating debt ratios. This assumes that
market value debt ratios are always lower than book value debt ratios, an assumption not
based on fact. Furthermore, even if the market value debt ratios are lower than the book
value ratios, the cost of capital calculated using book value ratios will be lower than those
calculated using market value ratios, making them less conservative estimates, not more.
To illustrate this point, consider Amazon. The firm’s market value of equity of $17.26
billion and the market value of debt of $1.345 billion yield a market debt ratio of 7.81%.
In contrat, using Amazon’s book values for equity ($266.28 million) and debt ($1480.66
47
million) results in book debt ratio of 84.76%. The cost of capital can be calculated as
follows –
With market value debt ratios:
12.94% (.9219) + 8% (.0781) = 12.56%
With book value debt ratios: 12.94% (.1524) + 8% (.8476) = 8.75%
Third, it is claimed that lenders will not lend on the basis of market value, but
this claim again seems to be based more upon perception than fact. Any homeowner who
has taken a second mortgage on a house that has appreciated in value knows that lenders
do lend on the basis of market value. It is true, however, that the greater the perceived
volatility in the market value of an asset, the lower is the borrowing potential on that
asset.
There is one important point to be made about market values. Market prices for
equity can change a great deal from period to period for technology firms. Amazon’s
market value of equity would have been $ 33 billion if this analysis had been done three
months earlier, and the debt ratio would have been lower. The effect on the cost of capital
will be muted, however, because technology firms tend to have small amounts of debt on
their balance sheets. Even Amazon, which has a lot of debt for a new technology firm,
has only seen its debt ratio increase from 4% to 7.81%, even as its equity market value
22
There are some who argue that stock prices are much more volatile than the underlying true value. Even
if this argument is justified (and it has not conclusively been shown to be so), the difference between market
value and true value is likely to be much smaller than the difference between book value and true value.
48
dropped by 50%. With a cost of equity of 12.94% and a cost of debt of 8%, the cost of
capital has changed from 12.74% to 12.56% as the debt ratio has increased23.
Estimating the Market Values of Equity and Debt
The market value of equity is generally the number of shares outstanding times
the current stock price. If there other equity claims in the firm such as warrants and
management option, these should also be valued and added on to the value of the equity
in the firm.
The market value of debt is usually more difficult to obtain directly, since very
few firms have all their debt in the form of bonds outstanding trading in the market. Many
firms have non-traded debt, such as bank debt, which is specified in book value terms but
not market value terms. A simple way to convert book value debt into market value debt
is to treat the entire debt on the books as one coupon bond, with a coupon set equal to the
interest expenses on all the debt and the maturity set equal to the face-value weighted
average maturity of the debt, and then to value this coupon bond at the current cost of
debt for the company. Thus, the market value of $ 1 billion in debt, with interest expenses
of $ 60 million and a maturity of 6 years, when the current cost of debt is 7.5% can be
estimated as follows:


1
(1 
6 
(1.075)  1,000
Estimated Market Value of Debt = 60 
 .075
 (1.075)6  $930




23
The effect would be even smaller if you adjusted the beta for the higher debt to equity ratio that Amazon
has after the drop in market value of equity.
49
While this will yield a market value for the debt in the balance sheet, it still
ignores other commitments that a firm has made that should be categorized as debt. The
most important of these is operating leases. When a lease is classified as an operating
lease, the lease expenses are treated as operating expenses and the operating lease does
not show up as part of the debt of the firm. When a lease is classified as a capital lease,
the present value of the lease expenses is treated as debt, and interest is imputed on this
amount and shown in the income statement. You could make the argument that in an
operating lease, the lease payments are just as much a commitment as are lease expenses
in a capital lease or interest payments on debt. Converting operating lease expenses into a
debt equivalent is straightforward. The operating lease commitments in future years,
which are revealed in the footnotes to the financial statements for US firms, should be
discounted back at a rate that reflects their status as unsecured and fairly risky debt. As an
approximation, using the firm’s current pre-tax cost of borrowing as the discount rate
yields a good estimate of the value of operating leases
Illustration 3.6: Difference between market value and book value debt ratios
The following table contrasts the book values of debt and equity with the market
values for Cisco, Motorola, Amazon and Ariba. Rediff has no debt on its books. For the
four publicly traded firms, the market value of equity is estimated using the current
market price and the number of shares outstanding. For Rediff.com, you use the book
value of equity, but the absence of debt makes the debt ratio zero. Cisco has no
conventional debt, but Motorola, Amazon and Ariba do have debt on their books. All of
these firms except for Motorola also have operating lease commitments, and these
commitments are treated as debt.
50
You estimate the market value of debt using the book value of debt, the interest
expense on the debt, the average matuirty of the debt and the pre-tax cost of debt for each
firm. For Motorola, the book value of debt is $5,593 million, the interest expense on the
debt is $ 305 million, the average maturity of the debt is 3.26 years and the pre-tax cost of
debt is 6.50%. The estimated market value is as follows:


1
(1
3.26 
5,593
(1.065) 
Estimated MV of Motorola Debt = 305


 (1.065) 3.26  $5,426 million
.065




Since Motorola has no operating lease commitments, the estimated market value of
Motorola’s debt is $5,426 million.
Ariba has a small amount of conventional debt ($1.47 million) on its balance
sheet, which is at market value. To this amount, you add the present value of operating
lease commitments that Ariba has over the next 5 years, with the cost of debt of 9.25%
used as the discount rate. Table 3.8 presents the debt value of operating leases.
Table 3.8: Debt Value of Operating Leases: Ariba
Year
1
2
3
4
5
6 and beyond24
Total Present Value =
Lease Commitment Present Value at 9.25%
$
5.10
$
4.67
$
5.20
$
4.35
$
5.29
$
4.06
$
5.40
$
3.79
$
5.42
$
3.49
$
9.78
$
5.75
$ 26.10 million
The cumulative market value of debt for Ariba is $27.57 million.
24
The 10-K reports on the cumulated value of operating leases after year 6. In this case, you have assumed
that the entire payment is in year 6. If the amount had been larger, you would have treated it as an annuity
over multiple years for computing the present value.
51
You estimate the market values of debt and operating leases for Amazon and
Cisco, using a similar approach. Table 3.9 summarizes the final estimates of value for all
of the firms.
Table 3.9: Comparison of Book Value and Market Value Debt Ratios
Motorola
Cisco
Amazon
Ariba
Rediff.com
BV of Debt
5,593
0
1481
1.47
0
BV of Equity
16,828
11,722
266
122.18
0.29
BV D/(D+E)
24.95%
0%
84.76%
1.19%
0%
MV of Equity
73,706
446,989
17,237
17,832
NA
MV of Debt
5,426
0
1345
1.47
0
PV: Leases
0
827
114
26.1
0
6.86%
0.18%
7.81%
0.15%
0%
MV D/(D+E)
wacccalc.xls: This spreadsheet allows you to convert book values of debt into market
values.
Estimating the Cost of Capital
Since a firm can raise its money from three sources -- equity, debt and preferred
stock -- the cost of capital is defined as the weighted average of each of these costs. Thus,
if E, D and PS are the market values of equity, debt and preferred stock respectively, the
cost of capital can be written as follows:
Cost of Capital = ke ( E/ (D+E+PS)) + kd ( D/ (D+E+PS)) + kps ( PS/ (D+E+PS))
Illustration 3.7: Estimating Cost of Capital
Concluding the analysis in this chapter, you estimate the costs of capital for each
of the five firms that you will be valuing.
Table 3.10: Cost of Capital Calculation
52
Motorola
Cisco
Amazon
Ariba
Rediff.com
Cost of Equity
10.85%
11.72%
12.94%
13.12%
25.82%
Equity/(Debt + Equity)
93.14%
99.82%
92.19%
99.85%
100%
Cost of Debt
4.23%
4.03%
8.00%
9.25%
10.00%
Debt/(Debt + Equity)
6.86%
0.18%
7.81%
0.15%
0%
Cost of Capital
10.39%
11.71%
12.56%
13.11%
25.82%
Note that the costs of capital are close to the costs of equity for all of the firms, and
almost identical to them for three. This is because equity dominates the capital structures
for all of the firms, but especially the youngest - Ariba and Rediff.com.
Summary
The costs of equity and capital are fundamental inputs in discounted cash flow
valuation and the estimation problems can be far greater when you look at technology
firms. In this chapter, you consider the estimation issues and suggest solutions to some of
the more common shortcomings.
Risk and return models for estimating the cost of equity begin with the premise
that the marginal investor is well diversified and is therefore concerned only about the
risk added by an investment on to a diversified portfolio. This added risk is measured
differently in different models, ranging from a market beta in the capital asset pricing
model to proxies such as market capitalization in proxy models. This view of risk is
justified for technology firms, even though many of them continue to be closely held and
run by their founders. This is because institutional investors, who tend to be well
diversified, tend to dominate trading in these stocks. The standard procedures for
estimating risk parameters, however, have to be modified substantially both because of
these firms’ limited and volatile price histories and because of the changes that these
firms can go through in short periods. Bottom-up betas, based upon the businesses that
the firms operate in, are an alternative to regression betas and usually have lower standard
53
error and better reflect your firm’s current standing. In addition, the cost of equity should
be estimated using implied, rather than historical premiums, and should be based upon
long term riskless rates, rather than short term ones.
When technology firms borrow money, they often use hybrid securities such as
convertible bonds. Furthermore, they are often unrated, leaving you with the task of
estimating ratings based upon one or two years of history.
As a final point, it is worth noting that the costs of debt and equity, the weights on
each and the resulting cost of capital will change over time for all firms, but especially so
for young high-growth firms. Consequently, you need to not only estimate the current
cost of capital but forecast how the costs of debt, equity and capital will change as the
firm grows larger and more stable.